The realization of controllable fermionic quantum systems via quantum simulation is instrumental for exploring many of the most intriguing effects in condensed-matter physics^1,2,3. Semiconductor quantum dots are particularly promising for quantum simulation as they can be engineered to achieve strong quantum correlations. However, although simulation of the Fermi–Hubbard model⁴ and Nagaoka ferromagnetism⁵ have been reported before, the simplest one-dimensional model of strongly correlated topological matter, the many-body Su–Schrieffer–Heeger (SSH) model^{6,7,8,9,10,11}, has so far remained elusive—mostly owing to the challenge of precisely engineering long-range interactions between electrons to reproduce the chosen Hamiltonian. Here we show that for precision-placed atoms in silicon with strong Coulomb confinement, we can engineer a minimum of six all-epitaxial in-plane gates to tune the energy levels across a linear array of ten quantum dots to realize both the trivial and the topological phases of the many-body SSH model. The strong on-site energies (about 25 millielectronvolts) and the ability to engineer gates with subnanometre precision in a unique staggered design allow us to tune the ratio between intercell and intracell electron transport to observe clear signatures of a topological phase with two conductance peaks at quarter-filling, compared with the ten conductance peaks of the trivial phase. The demonstration of the SSH model in a fermionic system isomorphic to qubits showcases our highly controllable quantum system and its usefulness for future simulations of strongly interacting electrons.

通过量子模拟实现可控费米子量子系统有助于探索凝聚态物理中许多最有趣的效应^1,2,3 。半导体量子点对于量子模拟特别有前景，因为它们可以被设计来实现强量子相关性。然而，尽管之前已经报道过费米-哈伯德模型⁴和长冈铁磁性⁵的模拟，但最简单的强相关拓扑物质一维模型，多体 Su-Schrieffer-Heeger (SSH) 模型^{6,7,8 ,9,10,11} ，迄今为止仍然难以捉摸——主要是由于精确设计电子之间的长程相互作用以重现所选哈密顿量的挑战。在这里，我们表明，对于具有强库仑约束的硅中精确放置的原子，我们可以设计至少六个全外延面内栅极来调整十个量子点线性阵列上的能级，从而实现微不足道的和多体 SSH 模型的拓扑阶段。强大的现场能量（约 25 毫电子伏）以及在独特的交错设计中以亚纳米精度设计门的能力使我们能够调整单元间和单元内电子传输之间的比率，以观察具有两个电导峰值的拓扑相的清晰特征。四分之一填充，与平凡阶段的十个电导峰相比。在与量子位同构的费米子系统中演示 SSH 模型，展示了我们高度可控的量子系统及其对于未来强相互作用电子模拟的有用性。